\(A=5+5^2+5^3+...+5^{2015}\)
\(\Rightarrow5A=5^2+5^3+5^4+...+5^{2016}\)
\(\Rightarrow5A-A=\left(5^2+5^3+5^4+...+5^{2016}\right)-\left(5+5^2+5^3+...+5^{2015}\right)\)
\(\Rightarrow4A=5^{2016}-5\)
Mà \(4A+5=25^x\)
\(\Rightarrow5^{2016}-5+5=25^x\)
\(\Rightarrow5^{2016}=25^x\)
\(\Rightarrow\left(5^2\right)^{1008}=25^x\)
\(\Rightarrow25^{1008}=25^x\)
\(\Rightarrow x=1008\)
Vậy x = 1008
A=5+5^2+5^3+...+5 ^2015
=> 5A=5^2+5^3+...+5^2016
=> 5A-A=(5^2+5^3+...+5^2016)-(5+5^2+5^3+...+5 ^2015)
=> 4A=5^2016-5
=> A=\(\frac{5^{2016}-1}{4}\)
Thay vào
25^x=4A+5
=> 25^x=\(\frac{5^{2016}-1}{4}+5\)
